Lecture Notes: Intersection Collision

Introduction

• Discussion on the collision of two cars at an intersection.
• After collision, cars are locked and move together at an angle.
• Given:
  • Angle of movement post-collision: 20 degrees
  • Common speed post-collision: 30 m/s

Objective

• Determine the initial speed of car one and car two.
• Identify which car was driving faster.

Key Concepts

• Conservation of Linear Momentum
• Vector Resolution: Resolving velocity into rectangular components.

Collision Details

• Mass of car 1: 1000 kg
• Mass of car 2: 1500 kg
• After collision:
  • Common velocity: 30 m/s
  • Direction: 20 degrees with respect to car 1's initial direction

Methodology

1. Conservation of Linear Momentum:

   • Total momentum is conserved in both elastic and inelastic collisions.
   • This is a perfect inelastic collision (cars lock together).

2. Equations Used:

   • Apply momentum conservation along the x-axis and y-axis.

X-axis Calculation

• Before Collision:

  • Car 1 momentum: ( m_1 \times v_1 )
  • Car 2 has no x-component momentum.

• After Collision:

  • Combined momentum: ( (m_1 + m_2) \times v \cos(\theta) )

• Solve for v1:

  • ( v_1 = \frac{(m_1 + m_2) \times v \cos(\theta)}{m_1} )
  • Result: ( v_1 = 70.5 \text{ m/s} )

Y-axis Calculation

• Before Collision:

  • Car 1 has no y-component momentum.
  • Car 2 momentum: ( m_2 \times v_2 )

• After Collision:

  • Combined momentum: ( (m_1 + m_2) \times v \sin(\theta) )

• Solve for v2:

  • ( v_2 = \frac{(m_1 + m_2) \times v \sin(\theta)}{m_2} )
  • Result: ( v_2 = 17.1 \text{ m/s} )

Conclusion

• Car 1 was moving faster than Car 2 pre-collision.
• The analysis shows how to determine the speed of vehicles involved in a collision using conservation of momentum.
• Useful in accident investigation.

Closing

• Encouragement to ask questions and engage with the content.
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